Pass Your GCSE Maths Exams

What Is A Function?

FunctionsMany equations describe a real-life relationship between two quantities, also known as function. The function is said to be the central idea in the study of mathematics.

A \(\underline{function}\) is a specific rule that compares one quantity to another quantity. The correspondence between two variables, the x and y, use a set of ordered pairs (x, y) to show that the x is related to y. The interrelation between number patterns or ordered pairs can be represented, graphs, and equations. An example of a function is one that shows the relationship between the employee salary (x) to the number of hours work (y). Another example is (x) water bill paid for a month and its relationship to the cubic meters of water consumed (y) plus other charges (k).Example:Observe the following ordered pair
a. {(1, 2), (2, 3), (3, 4), (4, 5)}
b. {(2, 3), (1, 5), (3, 7), (3, )}

The relation between the ordered pair in this example is a function. Looking at the value of x, there is no ordered pair with the same first element.

b. {(2, 3), (1, 5), (3, 7), (3, 9)}
x y
2 3
1 5
3 7
3 9

This is not a function since the first element, which is 3, corresponds to the different second elements, which are 7 and 9.

Function NotationFunction notation is the functional relationship between two variables such x and y. It is represented by this equation:
y = f(x) Read as y equals function of x, or y is a function of x. It means that the value of y depends on the value of x. Thus, x is an independent variable while y is a dependent variable.